Allow custom icon in <SearchItemIcon/> #71491

What problem does this address?

In the <SearchItemIcon />, it would be nice to be able to use an icon for a custom post type. Right now it appears that only built-in post types are allowed.

https://github.com/WordPress/gutenberg/blob/trunk/packages/block-editor/src/components/link-control/search-item.js

What is your proposed solution?

Either allow the ICONS_MAP to be filtered, the final icon to be filtered, or allow a way to register the icon in the register_post_type and send it along with REST Response?